Base field 3.3.1345.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[25, 25, -w^{2} - w + 5]$ |
| Dimension: | $10$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{10} - 33x^{8} + 376x^{6} - 1765x^{4} + 2900x^{2} - 400\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -w - 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, w + 2]$ | $\phantom{-}\frac{17}{500}e^{8} - \frac{433}{500}e^{6} + \frac{156}{25}e^{4} - \frac{241}{20}e^{2} - \frac{8}{5}$ |
| 7 | $[7, 7, w + 3]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w + 2]$ | $-\frac{2}{125}e^{9} + \frac{48}{125}e^{7} - \frac{59}{25}e^{5} + \frac{9}{5}e^{3} + \frac{42}{5}e$ |
| 7 | $[7, 7, -w + 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}\frac{31}{1000}e^{9} - \frac{819}{1000}e^{7} + \frac{323}{50}e^{5} - \frac{691}{40}e^{3} + \frac{68}{5}e$ |
| 13 | $[13, 13, -w^{2} + w + 4]$ | $\phantom{-}\frac{17}{1000}e^{9} - \frac{433}{1000}e^{7} + \frac{78}{25}e^{5} - \frac{261}{40}e^{3} + \frac{37}{10}e$ |
| 19 | $[19, 19, -w^{2} + 5]$ | $-\frac{14}{125}e^{8} + \frac{361}{125}e^{6} - \frac{538}{25}e^{4} + \frac{237}{5}e^{2} - \frac{36}{5}$ |
| 23 | $[23, 23, -w^{2} - w + 3]$ | $-\frac{1}{50}e^{9} + \frac{29}{50}e^{7} - \frac{27}{5}e^{5} + \frac{187}{10}e^{3} - 19e$ |
| 27 | $[27, 3, 3]$ | $-\frac{9}{500}e^{9} + \frac{241}{500}e^{7} - \frac{97}{25}e^{5} + \frac{41}{4}e^{3} - \frac{19}{5}e$ |
| 29 | $[29, 29, w^{2} - w - 3]$ | $\phantom{-}\frac{1}{500}e^{8} - \frac{49}{500}e^{6} + \frac{33}{25}e^{4} - \frac{73}{20}e^{2} - \frac{24}{5}$ |
| 31 | $[31, 31, w^{2} - w - 8]$ | $\phantom{-}\frac{3}{250}e^{8} - \frac{97}{250}e^{6} + \frac{103}{25}e^{4} - \frac{149}{10}e^{2} + \frac{36}{5}$ |
| 37 | $[37, 37, -w - 4]$ | $-\frac{3}{250}e^{9} + \frac{36}{125}e^{7} - \frac{91}{50}e^{5} + \frac{23}{10}e^{3} + \frac{33}{10}e$ |
| 43 | $[43, 43, 2w^{2} - 4w - 3]$ | $\phantom{-}\frac{11}{125}e^{9} - \frac{289}{125}e^{7} + \frac{452}{25}e^{5} - \frac{238}{5}e^{3} + \frac{184}{5}e$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-\frac{3}{500}e^{9} + \frac{47}{500}e^{7} + \frac{6}{25}e^{5} - \frac{113}{20}e^{3} + \frac{52}{5}e$ |
| 53 | $[53, 53, 2w^{2} - w - 11]$ | $-\frac{31}{500}e^{9} + \frac{769}{500}e^{7} - \frac{511}{50}e^{5} + \frac{247}{20}e^{3} + \frac{283}{10}e$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $-\frac{1}{250}e^{8} + \frac{49}{250}e^{6} - \frac{66}{25}e^{4} + \frac{103}{10}e^{2} - \frac{12}{5}$ |
| 67 | $[67, 67, w^{2} + w - 8]$ | $-\frac{9}{500}e^{9} + \frac{241}{500}e^{7} - \frac{92}{25}e^{5} + \frac{129}{20}e^{3} + \frac{46}{5}e$ |
| 71 | $[71, 71, w^{2} + w - 11]$ | $-\frac{2}{25}e^{8} + \frac{48}{25}e^{6} - \frac{59}{5}e^{4} + 12e^{2} + 12$ |
| 73 | $[73, 73, -w^{2} + 4w - 2]$ | $-\frac{11}{250}e^{9} + \frac{132}{125}e^{7} - \frac{317}{50}e^{5} + \frac{31}{10}e^{3} + \frac{241}{10}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -w - 1]$ | $-1$ |